Overfilled arch-shaped load support structure



Dec. 9, 1969 A. SCHUPPISSER ET AL 3,482,406

OVERFILLED ARCH-SHAPED LOAD SUPPORT STRUCTURE Filed Aug. 14, 1967 InVQDtU/S:

United States Patent Office 3,482,406 Patented Dec. 9, 1969 3,482,406OVERFILLED ARCH-SHAPED LOAD SUPPORT STRUCTURE Armin Schuppisser,Bassersdorf, and Werner Heierli, Zurich, Switzerland, assiguors toHeierli & C0., Zurich, Switzerland Filed Aug. 14, 1967, Ser. No. 660,430Claims priority, application Switzerland, Aug. 18, 1966, 11,952/66; July6, 1967, 9,691/67 Int. Cl. E01g 5/04; E21d 11/08; E04b 1/32 U.S. Cl.61-16 5 Claims ABSTRACT OF THE DISCLOSURE This invention discloses anoverfilled archshaped load support structure constructed as an arcuateor curved shell or one which is formed from flat slabs in aconfiguration approximating a curved shell, and which comprisespre-fabricated reinforced concrete components or reinforced concretecompounds cast at the construction site.

The present invention relates to an overfilled archshaped load supportstructure formed as a curved shell or from flat slabs in an arrangementapproximating to a curved shell, and comprising pre-fabricatedreinforced concrete components or reinforced compounds cast in situ.

The support structure may for example be an overfilled overpass orunderpass bridging over a lower tr-affic route and supporting an uppertraffic route. Any embankment material which can be used for roadembankments is suitable for the overfill.

With this structure the advantages resulting from the shape of the shellor the like, i.e. deformability and high load support by the overfill,are obtained with a small amount of material. The overfill serves todistribute the load and support the shell and therefore counteractsexcessive deformation of the shell structure.

If the structure is for example an overpass or an underpass, then for agiven inclination of the ramps and a given headroom for the underpassthe adjoining em bankment for the overpass can be higher and longer orthe cutting for the underpass can be deeper and longer as the overfillis made higher.

According to the usual laws of statics according to the state of theart, the rule was previously followed that the overfill at the highestpart of such a load support structure must be at least 4 of the radiusof curvature of the shell (or of the radius of the inner circle or outercircle of an outline of joined flat lines approximating to an arc). Withthe angle of e.g. 110 usually subtended by the are at its centre, theoverfill at the highest part of the support structure is more than /2(one half) times the intended height of the arc.

It is therefore evident that the height of the overfill, i.e. thedifference in height between the highest, outer part of the supportstructure and the upper e.g. horizontal plane of the overfill is animportant factor in the construction costs. In most cases the making ofan un derpass support structure with an overfilled arch-shaped loadsupport structure according to the above-mentioned previously employedrules with small constructional volume (thickness) was practicallyimpossible because of the large overfill required.

It is an object of the invention to reduce construction costs and/or toenable the use of an overfilled arch in the above-mentioned cases.

The present invention provides an overfilled archshaped load supportstructure formed as a curved shell or the ike and comprisingprefabricated reinforced concrete components or reinforced concretecomponents cast in situ, wherein the thickness of the load supportstructure with a cylindrical curvature is less than l th of the radiusof curvature thereof and with a non-cylindrical curvature is less than 4th of the largest radius of curvature thereof, and the height of theoverfill at the highest part of the support structure with a cylindricalcurvature is smaller than th of the radius of curvature thereof and witha non-cylindrical curvature is smaller than th of the largest radius ofcurvature thereof.

If a line on the periphery at the highest part of the structure does notextend parallel to the overfill, the above limiting values for theoverfill apply at the position at which this line has its smallestspacing from the overfill.

The horizontal upper limit of the overfill may be a plane approximatelytangential to the shell or the like (the overfill at the highest pointbeing e.g. only a few centimetres) According to the above-mentionedpreviously binding rules from the prior art, and which have heretoforebeen strictly adhered to in the prior art, such structures should nothave sufficient load supporting capacity. However, the considerations onwhich the invention is based indicate, and the experiments describedbelow confirm, that there is no reason for applying the above-mentionedpreviously usual dimension and construction rules of constructionalengineering and earth mechanics to structures of the present type.

Likewise, the same holds true with reference to the previously bindingrule according to which an embankment extending parallel to a tangentialplane of the support structure with an inclination of at most 1:4 musthave a spacing of at least of the radius of curvature from thetangential plane and an even greater spacing for steeper slopes. Theconsiderations and experiments underlying the invention have moreovershown that such an embankment can have an inclination of 1:1 to 1:4 andthe spacing of the plane of the embankment from the part nearest theretoof the support structure may be as little as A1 of the radius ofcurvature (or of the greatest radius of curvature for non-cylindrical,especially clothoidshaped arches, [dtv-Lexikon, volume 10, p. 185,Munich, Germany, 1967], that is Cornu spiral shaped arches).

Since there is less overfill according to the invention than with thepreviously employed accepted rules, the construction costs areconsiderably reduced. In this way the cost of an underpass can forexample be reduced to 70% of the previous amount.

The invention will be more readily understood from the followingdescription, given by way of example, of the embodiments thereofillustrated in the accompanying drawing, in which:

FIG. 1 shows a perspective view of an underpass according to theinvention;

FIG. 2 shows a dimension sketch of the structure of the invention inheavy lines and the comparable prior art in dotted lines;

FIG. 3 shows a special non-circularly curved arch shape for thestructure of the invention;

FIG. 4 shows a diagrammatic front elevation of an underpass according tothe invention with twin arches; and

FIG. 5 shows a cross-section through a foundation for the underpass ofFIG. 4

As shown in FIG 1 a traffiic route (wh ch in the present case is a roadbut which may alternatively be a railway, a river or a canal) has acutting (not shown) which is lower than a traffic route 2, and theoverfill of the underpass is indicated by reference numeral 3. Theunderpass has a load support structure 4 in the form of an arch andcomprising pre-fabricated reinforced concrete clements which are curvedin accordance with the radius of curvature of the arch and which may beconneted together as described in copending patent application SerialNo. 636,779 filed May 8, 1967.

The load support structure 4 is supported directly (i.e. withoutsupporting walls) on a plurality of separate foundations or strip shapedfoundations or on connecting beams of a pile foundation. The loadsupport structure 4 is shaped as part of a circularly cylindrical sleevethe thickness of which (i.e. the thickness of the reinforced concreteslabs 5) is about of its radius. The height of the overfill, in theexample illustrated, at the highest point of the load support structure4 is about of the radius of curvature of the arch, which in practice isabout 50 cm. The road surface of the upper traflic route may, at thehighest point of the load support structure 4, lie directly on the loadsupport structure 4, the upper limit of the overfill being a planetangential to the arch.

The load support structure 4 at the ends of the tunnel is inclined atthe same angle as the slope 3 and is formed at these positions ofreinforced concrete slabs triangular or trapezoidal shape, thetrapezoidal-shaped slabs having two right angles, which slabs are formedand connected to adjacent slabs as described above. It has been foundthat the inclined ends of the arch are sufficiently rigid and can beretained sufliciently by the remaining parts of the arch to retain theslope 3, and that it is sufficient to connect the inclined endspivotally or resiliently in a groove in the foundation. At the outerparts of the inclined ends, a foundation may be omitted.

The line of intersection of the plane of the slope 3 with the plane ofthe traific route 2 may intersect the longitudinal axis of the trafiicroute 1 at an acute angle of e.g. 45.

One advantageous example of the above-described underpass has thefollowing dimensions: radius of curvature of arch 7.5 metres; thicknessof slabs 16 centimetres, clearance height of surface support structureat crown 5.30 metres; height of embankment above crown 60 centimetres;width of upper road 15 metres. This underpass would be loaded on an area7 metres long (in the direction of the upper road) and 4 metres wide atthe edge With 370 tons. No unacceptable deformation is caused thereby.This is not, however, the load limit of the structure which, throughlack of suitable loads and because of difliculties in providing andtransporting them, Was not determined, although the loading mentionedabove corresponds to a multiple of the maximum heavy road loads.

In FIG. 2. the overfills which can be used according to the inventionare indicated by a broken line and the height of the overfill above thecrown of the arch, the inclination of a slope parallel to the tagentialplane of the arch and the spacing thereof from the arch are indicated inproportion to the radius of curvature r of the arch. The broken line andthe magnitudes associated therewith indicate the above-mentioned priorart.

The above-described surface structure, instead of being made of curvedslabs, may be composed of flat slabs, in which case the structurecomprises a series of fiat surfaces which approximate to a curved arch.Flat slabs can be made more simply and with higher concrete quality, areeasier to store and transport, and can be used for structures havingwidely varying arch radii of curvature. The slabs sutiably have, in theperipheral direction of the arch, a width of 1.6 to 2.3 m., preferably2. m.

The cross-section of the arch may be circularly curved or may haveapproximately the shape of a crown portion of a clothoid, also known asa cornu spiral, (FIG. 3), the radius of curvature decreasing from theupper, middle part outwardly. This shape has the advantage that theheight of the structure is very small and that the weight of the supportstructure produces only compression and no significant bending pigmentsin the support structure.

An arch shape which is particularly suitable as regards both the staticforces and also the profile of its opening is described below withreference to FIG. 3, which shows half of an arch of which the upper,middle part is a circular arc, which at each end meets a clothoid havinga radius which decreases outwardly. The half of the circular areillustrated at b, the end of the circular arc by c. O is the origin ofthe co-ordinate systems x, y of the clothoid and O is the vertex of thearch, i.e. the middle of the circular arc of which only one half (b) isshown. y is the perpendicular bisector of the chord s (of which onlyhalf is shown) of the circular arc and also the line of symmetry of thearch, and x is the tangent at the point 0 0 lies at the side of theperpendicular bisector y opposite the clothoid c above x the spacing of0 from y being about 0.0841 and from x about 0.015a. y and y divergedownwardly at an angle of about 4 new degrees (corresponding to about336 a is defined at least approximately by the equation R=2.4a in whichR is the radius of the circular arc. The clothoid is defined at leastapproximately by the equation rL=a where r is the radius of curvature ofthe clothoid and L the spacing from 0 measured along the clothoid. Atpoint B, R=r.

The undespass described above may also be made with a plurality ofarches or the like. FIG. 4 shows one example of this type with a supportstructure formed as a twin arch supported in the middle by a pendulumwall.

FIG. 5 shows a front view of a modification of the foundation for theouter end of the twin arch. This foundation, which can be used forexample for the underpass shown in FIG. 1, has the shape of a prism madefrom concrete and having a cross-section which is approximately aright-angled triangle. The widest side 6 lies on ground inclinedapproximately prependicular to the tangent to the arch end 4.Advantageously, this Widest side has the inclination which usuallyremains on excavation of the ground. One of the smallest sides 7 extendsperpendicularly or outwardly inclined and forms a part of the inner wallsurface of the underpass, and the other side 8 extends, as shown in thedrawing, inclined upwardly from the left to the right. This foundationcan be made without reinforcement and is only subjected to a pressurewhich spreads through the triangular cross-section. If the surface 8 isapproximately horizontal, the construction of this foundation requires aconnection only to the side 7, which can be effected either withconnection panels or as a formwork of prefabricated concrete slabs.

The support structure described above having one or more arches, e.g. atwin arch, can also be made of concrete cast. in situ, the latterconstruction preferably requiring less contra-casing than acorresponding single arch. Each arch can also be prefabricated in onepiece at the building site.

The support structure described above as an example for two underpassesis considerably less costly than a corresponding prior art supportstructure. Moreover, the lower overfill is frequently advantageous. Forexample, in an overpass or an underpass the construction costs mainlydepend, as mentioned above, on the height of the overfill, since theheight of the embankment or the depth of the cutting and lengths of theramps (for a given slope) depend on'tlie height of the overfill. For anunderpass on a hillside or at an acute-angled crossing of two traflicroutes the costs-are increased if the inclination of the slope on thevalley side in the first case or parallel to the upper traffic route inthe second case is small or if the spacing from the clearance space ofthe underpass is large. Corresponding relationships hold true for otheroverfilled support structures.

Since the support structure is relatively thin, it adapts to settlingdifferences, shrinkages and temperature differences. (Expansion gaps maybe necessary only in the lon. gitudinal direction in long underpasses.)In particular, it has been found that the strength of the fill material.

limits the deformation of the support structure to acceptable limits.This can be brought about since the pressure exerted by the fillmaterial on the support structure at the points at which the supportstructure tends to cave inwardly decreases as the caving increases, andat the points at which the support structure tends to cave outwardlyincreases as the caving increases, and thus opposes any deformation.

The support structure suitably has a shape such that its own weightproduces mainly compressions and no significant tensions or bendingmoments in the support structure. When made of concrete cast in situ,there is the advantage that the shoring can be removed shortly after thecasting since the bending moments resulting from the weight of thesupport structure are small. Therefore no fractures occur even althoughthe age of the concrete is not great. A shape which is suitable for thispurpose is an at least approximately circular curvature subtending atits centre an angle of 50 to 100, and preferably 65 to 75. The clothoidshape, as mentioned above, is particularly suitable.

The ends of the support structure resting on the foundations preferablyhave an inclination of 35 to 55, and in particular 40 to 50, and in aconstruction having a plurality of arches the ends of the archessupported on pillars suitably have an inclination of 5 to 25, and inparticular to relative to the horizontal. Acute angled spaces forfilling, in which compacting of the fill material is difiicult and whichcause increased danger of collapse during construction due to thepossibility of landslides, are thereby avoided. Moreover, machinecompacting is facilitated. In this connection, the foundation shown inFIG. 5, which has an approximately horizontal side of e.g. 2 metreswidth, may also be advantageous.

The requirement in practice of providing a given clearance space with asmall height is fulfilled since the arch touches the upper corner of theclearance space, and in the case of twin arches the middle thereoftouches the upper edge of the clearance space. The space above thisupper edge, which does not involve additional costs is for example inlong motorway underpasses very useful for ventilation and enablestransportation of goods of abnormal height. The vertical faces 7 of thefoundations shown in FIG. 5, together with the adjoining sides of thearch, define a space which also does not necessitate additional costsand which can be used e.g. for pedestrians or side lanes and thesesurfaces may be dimensioned accordingly. In long motorway underpassesthis space is also useful for ventilation.

We claim:

1. An overfilled arch-shaped load support structure comprising arelatively thin curved shell of cementitious material curving upwardlyfrom a ground plane, fouuda' tion means on said ground plane, saidcurved shell having edge extremities supported by said foundation means,said curved shell having a cross-section comprising a central portion ofsubstantially cylindrical curvature comprising a circular arc ofsubstantially constant radius R integral with opposite end curvatureportions of non-cylindrical curvature, said non-cylindrical curvatureportions of said shell each defined by a non-circular curve having aradius r which progressively decreases in length outwardly toward theedge extremities according to the equation rL:a where R is approximatelyequal to 2.4a, L is the arcuate length of the non-circular curve takenfrom the origin of the co-ordinate system thereof, said origin beingspaced a distance of about 0.08a on the side opposite to theperpendicular bisector of the chord of the circular are from saidperpendicular bisector and lying about 0.0150: above the tangent at thecrown of the circular arc, the ordinate of said co-ordinate systemdiverging downwardly at an angle of approximately 4 new degrees withreference to the said perpendicular bisector and R being equal to r atthe ends of the circular are.

2. An overfilled arch-shaped load support structure as set forth inclaim 1 in which said curved shell has a thickness less than of saidradius R.

3. An overfilled arch-shaped load support structure as set forth inclaim 1 including overfill on said curved shell having a depth at thehighest part of the central portion: of the structure less than of thelongest or constant radius R.

4. A structure as claimed in claim 1, wherein the angle subtended at thecenter of the largest curvature of the central portion by the edgeextremities of the support structure resting on the foundations is to 5.,An overfilled arch-shaped load support structure comprising arelatively thin curved shell of cementitious material curving upwardlyfrom a ground plane, foundation means on said ground plane, said curvedshell having edge extremities supported by said foundation means,said-curved shell having a cross-section comprising a central portion ofsubstantially cylindrical curvature integral with opposite end curvatureportions of non-cylindrical curvature, said non-cylindrical curvatureportions of said shell having radii of progressively decreasing lengthstoward the edge extremities, said curved shell having a thickness lessthan A of the longest of the said radii of curvature thereof, overfillon said curved shell having a depth at the highest part of the centralportion of the structure less than /30 of the longest of the said radiiof curvature, said foundation means comprising longitudinally extendingunreinforced cementitious material cast in situ, the cross-section ofwhich is approximately a right-angled triangle the hypotenuse of whichis approximately perpendicular to the tangent at the end of the endcurvature portion and lies on the ground, one other side of the trianglebeing approximately vertical and forming a part of the inner surface ofthe support structure and the third side of the triangle being outwardlyinclined.

References Cited UNITED STATES PATENTS 997,382 7/1911 Foster 61-161,638,428 8/1927 Zander 6l16 X 2,536,759 l/1951 Martin et al 6l--16 X3,282,056 11/1966 Fisher 6l42 X FOREIGN PATENTS 38,633 4/1957 Poland.

FRANK L. ABBOTT, Primary Examiner PRICE C. PAW, JR., Assistant ExaminerUS. Cl. X.R.

